GNSS post positioning with selected precision

ABSTRACT

A computer apparatus for post positioning with a selected precision. The apparatus includes a GNSS post processor to post process reference GNSS carrier phases from a reference system and rover GNSS carrier phases from a rover receiver to compute a secure position for the rover receiver not available to a user. The apparatus includes a vector offset generator to use the selected precision to compute a dither level for offset vectors to degrade an intrinsic precision of the secure position to provide a user-available position for the rover receiver at the selected precision.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of application Ser. No.11/799,022 by Bird filed Apr. 30, 2007 now U.S. Pat. No. 7,468,693 whichis a continuation of application Ser. No. 11/138,223 by Bird filed May26, 2005 now U.S. Pat. No. 7,227,496 issued Jun. 5, 2007, all assignedto the same assignee.

BACKGROUND

1. Field of the Invention

The invention relates generally to positioning and more particularly topositioning with selected accuracy having high integrity.

2. Description of the Background Art

The Global Positioning System (GPS) is operated by the United Statesgovernment for providing free GPS positioning signals to all usersaround the world. Stand alone GPS receivers can use a coarse/acquisition(C/A) code in these signals for computing unaided positions havingtypical accuracies of about five to twenty meters. These accuracies aresufficient for some applications including most navigation applications.However, there are positioning applications, such as survey, mapping,machine control and agriculture, where greater accuracy or integrity isneeded.

Some of these needs are met by differential GPS systems that provide GPScode phase corrections. A GPS receiver that is constructed fordifferential GPS operation can use the code phase corrections forcomputing positions having typical accuracies of a few tens ofcentimeters to a few meters. These accuracies are sufficient for manypositioning applications. However, a user cannot be altogether confidentin the accuracies of stand alone or differential GPS positions becausethe integrity of the positions is affected by multipath. Multipathreflections of the GPS signals can cause occasional large errors of tensto hundreds of meters or even more depending on the extra distances thatare traveled by reflected signals.

Fixed ambiguity real time kinematic (RTK) systems provide highlyaccurate GPS carrier phase measurements in order to provide greateraccuracy and at the same time avoid most of the effects of multipath. Arover GPS receiver that is constructed for RTK operation can use thecarrier phase measurements for determining relative positions havingtypical accuracies of about a centimeter to a few tens of centimeters.The term “fixed ambiguity” refers to the fact that an integer number ofcycles of carrier phase is resolved (fixed) for the RTK carrier phasemeasurements between the reference phase and the phase measured by therover. The resolution of the carrier cycle integer traps multipathsignal errors that are greater than a portion of the wavelength of thecarrier of the GPS signal, resulting in a high confidence and integrityfor the RTK-based positions.

Existing GPS RTK systems provide fixed RTK carrier phase measurements tothe users for a cost that is largely driven by the fixed infrastructurecosts for providing the system divided by the number of users. However,some users require the integrity of fixed RTK-based positioning but donot require the full accuracy that it provides. Unfortunately, there isno existing technique for spreading the infrastructure costs across moreusers by providing high integrity positions with accuracies that arelower than the full accuracy of the system.

SUMMARY

The present disclosure describes ways of providing high integritypositioning with controlled accuracies for a rover station either byproviding synthetic reference phases for a GPS reference system or bydithering a secure rover position.

Briefly, several systems are disclosed using measurements of orincluding one or more real time kinematic (RTK) reference stations forreceiving GPS signals at one or more actual reference positions and formeasuring reference phases. When three or more reference stations areused, virtual reference phases may be determined for a virtual referenceposition. A synthetic offset vector is generated in a reference station,a server in the reference system, an RTK rover station, or a syntheticphase processor interacting between the reference stations and the roverstation. Reference phase measurements are used with the synthetic offsetvector for inferring synthetic reference phases for a synthetic positionwhere the synthetic position is not equal to any of the actual orvirtual reference positions. The rover station uses the actual orvirtual reference position with the synthetic reference phases in placeof the actual or virtual reference phases for computing a rover positionwith respect to the actual or virtual reference position having an addedpositional error that is proportional to the synthetic offset vector.

In another approach a secure RTK rover station uses a synthetic offsetvector directly for dithering a secure rover position determined fromthe actual or virtual reference phase. The synthetic offset vector maybe generated in a reference station, a server in the reference system,the rover station, or a processor acting between the reference systemand the rover station. The positions determined by the rover stationhave the integrity of the RTK system with accuracy controlled by thesynthetic offset vector.

One embodiment is a secure rover station having a controlled accuracyfor a geographical position, comprising: a rover global navigationsatellite system (GNSS) receiver for determining a secure position notavailable to a user of the rover station; and a position ditherprocessor for dithering the secure position with a selected non-zerosynthetic offset vector for issuing a rover position available to theuser having an added position error proportional to the synthetic offsetvector.

Another embodiment is a method for controlling accuracy of ageographical position, comprising: receiving a global navigationsatellite system (GNSS) signal; using the GNSS signal for determining asecure position not available to a user of the rover station; anddithering the secure position with a selected non-zero synthetic offsetvector for providing a rover position having an added position errorproportional to the synthetic offset vector to the user.

Another embodiment is a tangible medium containing a set of instructionsfor causing a processor to carry out the following steps for controllingaccuracy of a geographical position, comprising: receiving a globalnavigation satellite system (GNSS) signal; using the GNSS signal fordetermining a secure position not available to a user of the roverstation; and dithering the secure position with a selected non-zerosynthetic offset vector for providing a rover position available to theuser having an added position error proportional to the synthetic offsetvector.

Another embodiment is a computer apparatus for post positioning with aselected precision, comprising: a global navigation satellite system(GNSS) post processor to post process reference GNSS carrier phases froma reference system and rover GNSS carrier phases from a rover receiverto compute a secure position, not available to a user, for the roverreceiver; and a vector offset generator to use a selected precision tocompute a dither level for a sequence of offset vectors to degrade anintrinsic precision of the secure position to provide a user-availableposition for the rover receiver at the selected precision.

Another embodiment is a method for providing a selected precision for aposition, comprising: post processing reference GNSS carrier phases froma reference system and rover GNSS carrier phases from a rover receiverfor computing a secure position, not available to a user, for the roverreceiver; and computing a dither level for a sequence of offset vectorsfor degrading an intrinsic precision of the secure precision forproviding a user-available position at the selected precision for therover receiver.

Another embodiment is a computer-readable medium havingcomputer-executable instructions stored or carried thereby that whenexecuted by a processor, perform a method comprising steps of: postprocessing reference GNSS carrier phases from a reference system androver GNSS carrier phases from a rover receiver for computing a secureposition, not available to a user, for the rover receiver; and computinga dither level for a sequence of offset vectors for degrading anintrinsic precision of the secure precision for providing auser-available position at the selected precision for the roverreceiver.

These and other embodiments and benefits of the present invention willno doubt become obvious to those of ordinary skill in the art afterhaving read the following best mode for carrying out the invention andviewing the various drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a single reference system of the prior art forproviding reference phases to a rover station;

FIG. 1A is a diagram of a reference network positioning system of theprior art for providing reference phases to a rover station;

FIG. 2 is a diagram of a single reference positioning system forproviding synthetic reference phases to a rover station for adding aposition error to a rover position;

FIG. 2A is a block diagram of a reference station for the system of FIG.2;

FIG. 3 is a diagram of a reference network positioning system forproviding synthetic reference phases to a rover station for adding aposition error to a rover position;

FIGS. 3A, 3B and 3C are block diagrams of first, second and thirdembodiments of a server for the positioning system of FIG. 3;

FIG. 4 is a diagram showing a secure rover station for computingsynthetic reference phases for adding a position error to a roverposition operating in a single reference positioning system;

FIG. 4A is a block diagram of the rover station of FIG. 4;

FIG. 5 is a diagram showing a secure rover station for computingsynthetic reference phases for adding a position error to a roverposition in a reference network positioning system;

FIGS. 5A and 5B are block diagrams of first and second embodiments ofthe rover station of FIG. 5;

FIGS. 6A and 6B are block diagrams of first and second embodiments ofrandom reference generators for providing synthetic reference phases;

FIG. 7 is a diagram for a single reference positioning system where asecure rover station dithers a secure position for providing an unsecureposition having an added positional error;

FIGS. 7A and 7B are block diagrams of first and second embodiments ofthe positioning system of FIG. 7;

FIG. 8 is a diagram for a reference network positioning system where asecure rover station dithers a secure position for providing an unsecureposition having an added position error;

FIGS. 8A, 8B, 8C and 8D are block diagrams of first, second, third andfourth embodiments of the positioning system of FIG. 8;

FIG. 9 is a block diagram of a random position dither processor for thesystems of FIGS. 7 and 8;

FIG. 10 is a flow chart of a method for providing synthetic referencephases from a single reference positioning system to a rover station;

FIG. 11 is a flow chart of a method for providing synthetic referencephases from a reference network positioning system to a rover station;

FIG. 12 is a flow chart of a method for computing synthetic referencephases in a rover station operating in a single reference positioningsystem;

FIG. 13 is a flow chart of a method for computing synthetic referencephases in a rover station operating in a reference network positioningsystem;

FIG. 14 is a flow chart of the method for dithering a secure roverposition for providing an added error to a rover position in a singlereference positioning system;

FIG. 15 is a flow chart of the method for dithering a secure roverposition for providing an added error to a rover position in a referencenetwork positioning system;

FIG. 16 is a block diagram of a GNSS positioning system having areference system, a rover receiver, and a post processing computerapparatus;

FIG. 17 is a position diagram showing secure and user-available roverpositions for the rover receiver of FIG. 16;

FIG. 18 is a block diagram of the computer apparatus of FIG. 16;

FIG. 19 is a block diagram of a random process generator of the computerapparatus of FIG. 18;

FIG. 20 is a block diagram of a vector offset generator and a positiondither processor of the computer apparatus of FIG. 18;

FIG. 21 is a block diagram of a DOP scaler for the vector offsetgenerator of FIG. 20;

FIG. 22 is a flow chart of a method for providing a rover positionhaving a selected precision that is available to a user;

FIG. 23 is a flow chart of a method for generating an elongated sequenceof offset vectors for dithering a secure rover position;

FIG. 24 is a flow chart of a method for dithering a secure position forproviding a user-available position; and

FIGS. 25A and 25B are flow charts of a method for selecting auser-available precision based on a DOP of a secure position.

DETAILED DESCRIPTION

The details of several embodiments for carrying out the idea of theinvention will now be described. It should be understood that thedescription of these details is not intended to limit the invention tothese details. On the contrary these details are merely intended todescribe the best mode for carrying out the idea of the invention.Numerous alternatives, modifications and equivalents of the embodimentsdescribed herein will be apparent to someone skilled in the art aswithin the scope of the idea of this invention. An embodiment of theinvention is described for the global positioning system (GPS). However,it will be apparent to those in the art that the invention may becarried out with a generic global navigation satellite system (GNSS)including the global positioning system (GPS), the global orbitingnavigation system (GLONASS), the Galileo system or a combination ofthese systems. It should also be noted that pseudolites may be used inplace of satellites for broadcasting GNSS positioning signals.

FIG. 1 is a diagram showing a conventional real time kinematic (RTK)global positioning system (GPS)-based system of the prior art. Thereference station 12 includes a reference GPS receiver for receiving GPSsignals 14, illustrated as 14A, 14B and 14C, from GPS satellites 16,illustrated as 16A, 16B and 16C. The reference station 12 measures thecarrier phases of the GPS signals 14 and sends a radio signal 17 havingreference data for the measured phases and reference geographicalposition to one or more rover stations shown as rover 18. The roverstation 18 includes an RTK GPS receiver for measuring the carrier phasesfor the same GPS signals 14.

The difference between the reference and rover phase measurements yieldsestimates of perpendicular distance vectors represented by a vector dbetween the rover station 18 and the GPS satellite 16A. Measurementsfrom several GPS satellites 16 yield estimates of several perpendiculardistance vectors and ultimately the position of the rover station 18with respect to the reference station 12. The vector d may be understoodas a dot product of the vector between the GPS satellite 16 and therover station 18 and the vector between the reference station 12 and therover station 18. An exemplary RTK GPS system is described in U.S. Pat.No. 5,519,620, entitled “centimeter accurate global positioning systemreceiver for on-the-fly real-time-kinematic measurement and control” byNicholas C. Talbot et al., incorporated herein by reference.

FIG. 1A is a diagram showing a virtual reference system (VRS) RTKGPS-based system of the prior art. Reference network stations 12A, 12Bthrough 12N include reference GPS receivers for measuring carrier phasesof the GPS signals 14 received from the GPS satellites 16. The referencestations 12A-N send signals 22 having reference data for their measuredphases and reference geographical positions to a server 23. One of thereference stations, illustrated as 12A, is designated as a masterreference station. The server 23 and the master reference station 12Amay be located together. The server 23 communicates with one or more VRSRTK GPS rover stations with a radio signal 25. The VRS RTK GPS roverstations are shown as rover 24.

The server 23, or the server 23 together with the rover station 24,determine a virtual reference position 26 and a virtual vector 27between the position of the master reference station 12A and the virtualreference position 26; and then uses the position and measured phases ofthe master reference station 12A, the positions and measured phases ofthe auxiliary reference stations 12B-N and the virtual vector 27 (orvirtual reference position 26) to calculate virtual reference phases forthe virtual reference position 26 according to a virtual referencesystem (VRS) parametric model. The rover station 24 includes an RTK GPSreceiver for measuring the phases for the same GPS signals 14. Thedifference between the virtual reference and rover phase measurementsyields estimates of perpendicular distance vectors to the GPS satellites16 analogous to the vector d, described above, and ultimately theposition of the rover station 24 with respect to the virtual referenceposition 26.

The use of a network of reference stations instead of a single referenceallows modeling of the systematic ionosphere and troposphere parametricerrors in a region and thus provides the possibility of error reduction.Networks exist using public domain RTCM and CMR standards forbi-directional communication reference data to the rovers. Detailedinformation on the modeling of the errors is available in “VirtualReference Station Systems” by Landau et al., published by the Journal ofGlobal Positioning Systems for 2002, Vol. 1, No. 2 pages 137-143.

FIG. 2 is a diagram showing a real time kinematic (RTK) GPS-basedpositioning system referred to with a reference number 30. Thepositioning system 30 includes at least one reference station 31 forreceiving the GPS signals 14 from the GPS satellites 16. The referencestation 31 has a reference position that is established by a survey orsome other means. The system 30 receives or generates a synthetic offsetvector 32 for controlling the positioning accuracy that is provided bythe system 30 for one or more RTK GPS rover stations 118. The referenceposition and the synthetic offset vector 32 define a synthetic position33 where the synthetic position 33 is separated from the referenceposition by the synthetic offset vector 32. The length and direction ofthe synthetic offset vector 32 are arbitrary. However, it is normally afew meters or less.

FIG. 2A is a block diagram showing the reference station 31 and therover station 118. The reference station 31 includes a reference GPSreceiver 34, a synthetic phase processor 35 and a radio transceiver 36.The reference GPS receiver 34 and the synthetic phase processor 35 maybe separate or combined into a single unit. The radio transceiver 36 maybe a transmitter without a receiver if two-way transmission with therover station 118 is not required. The reference GPS receiver 34measures the carrier phases of the GPS signals 14. The processor 35 usesthe synthetic offset vector 32 with the reference position for thestation 31 and the three dimensional angles to the GPS satellites 16 forinferring the synthetic reference phases for the carrier phases thatwould be measured if the measurements were made at the syntheticposition 33.

The radio transceiver 36 sends a radio signal 37 having synthesizedreference data for the synthetic reference phases and the referenceposition to the rover station 118. Cellular or landline telephones maybe used to provide or to augment the radio signal 37. The synthesizedreference data still includes a correct geographical reference positionof the reference station 31, as is conventional, but the phases for theGPS signals 14 are not the actual phases that are measured at thereference position but are instead the synthetic reference phases thatare calculated from the measured reference phases, the actual referenceposition and the synthetic offset vector 32 (or synthetic position 33).

The rover station 118 includes a rover GPS receiver 119 and an anomalydetector 120. The rover GPS receiver 119 receives the GPS signals 14 andmeasures the carrier phases from the same GPS satellites 16 and computesthe differences between the measured rover phases and the syntheticreference phases. Using the synthetic reference phases in place of theactual reference phases, it now arrives at estimated perpendiculardistance vectors represented by the vector d* instead of the estimatedperpendicular distance vectors represented by the vector d describedabove. The vector d* may be understood as a dot product of the vectorbetween the GPS satellite 16A and the rover station 118 and the vectorbetween the synthetic position 33 and the rover station 118. When therover station 118 calculates its position with respect to the referencestation 31, it arrives at a position 38 that has an added positionalerror 39 of equal length in the opposite direction as the syntheticoffset vector 32. Using this technique the positioning system 30 is ableto arbitrarily introduce the added error 39 into the position 38 that iscalculated by the rover station 118.

The rover GPS receiver 119 determines double difference phase residualsfrom current and previous synthetic reference phases and current andprevious measured rover phases and passes the phase residuals to theanomaly detector 120. The anomaly detector 120 detects a phase residualanomaly when the phase residual is greater than a phase thresholdcorresponding to a selected distance for an integrity limit 40 for RTKoperation. The integrity limit 40 corresponds to an outer limit of azone about the rover position 38. When an anomaly is detected, theanomaly detector 120 inhibits the rover GPS receiver 119 from providingthe rover position 38 to the user of the rover station 118, or providesa notification to the user that the anomaly was detected and allows theuser to decide whether or not to use the position 38. Alternatively, theanomaly detector 120 provides a solution for the rover position 38 wherethe synthetic reference phase and measured rover phase for theparticular GPS signal 14 associated with the anomaly are not used. Theeffect of the system 30 is that the rover position 38 has the controlledadded position error 39 without degrading the integrity limit 40 of theRTK positioning solution of the rover position 38.

FIG. 3 is a diagram showing a network embodiment of a real timekinematic (RTK) GPS-based positioning system referred to by a referencenumber 50. The positioning system 50 includes a network of referencestations, referred to as 51A, 51B through 51N, for receiving the GPSsignals 14 from the GPS satellites 16. The reference network stations51A-N have reference positions established by a survey or some othermeans. The system 50 receives or generates a synthetic offset vector 32for controlling the positioning accuracy that is provided by the system50 for one or more RTK GPS rover stations shown as a rover station 124A,124B or 124C. The rover station 124A, 124B or 124C includes a rover GPSreceiver 125A, 125B or 125C, respectively, and an anomaly detector 126A,126B or 126C, respectively.

The positioning system 50 also includes a server 52A, 52B or 52C. Theserver 52A-C and the reference network stations 51A-N communicate withradio signals 54. One of the network stations, for example the station51A, may be designed as a master and the other reference networkstations 51B-N as auxiliaries. The master reference station 51A and theserver 52A-C may be co-located and may or may not share processingpower; or the master reference station 51A and the server 52A-C may bephysically separated.

The reference network stations 51A-N measure carrier phases of the GPSsignals 14 and then communicate their phase measurements to the server52A-C. The server 52A-C communicates with the rover station 124A-C witha radio signal 56. In a conventional system, the server 23 uses thevirtual vector 27 and the master and auxiliary reference positions andphases for determining the virtual reference phases for the virtualreference position 26. The sum of the virtual vector 27 and thesynthetic offset vector 32 is a master synthetic vector 64. The positionof the master reference station 51A and the master synthetic vector 64define a synthetic position 133. The system 50 uses the synthetic offsetvector 32 and the virtual vector 27 (or the master synthetic vector 64)and the master and auxiliary reference positions and phases fordetermining the synthetic reference phases for the synthetic position133.

The rover station 124A-C expects reference phases as if the phases aremeasured at the virtual reference position 26, however, it receives thesynthetic reference phases inferred for the synthetic position 133. Therover GPS receiver 125A-C receives the GPS signals 14 and measures thecarrier phases from the same GPS satellites 16; and computes thedifferences between the measured rover phases and the syntheticreference phases. Using the synthetic reference phases in place of thevirtual reference phases, it now arrives at estimated perpendiculardistance vectors represented by the vector d* as described above. Whenthe rover station 124A-C calculates its position with respect to thevirtual position 26, it arrives at the position 38 relative to thevirtual reference position 26 that has the added positional error 39that is equal in length and in the opposite direction as the syntheticoffset vector 32. Using this technique the positioning system 50 is ableto arbitrarily introduce the added error 39 into the position 38 that iscalculated by the rover station 124A-C.

The server 52A-C and the rover station 124A-C may use two-waycommunication to agree on the geographical position for the virtualreference position 26. For example, the virtual reference position 26may be selected to be the best estimated position of the rover station124A-C. It should be noted that the invention is not dependent on thelocation of the processing power of the server 52A-C. The processingpower of the server 52A-C may be located anywhere within communicationrange and may be distributed in several locations. Cellular or landlinetelephones may be used to provide or to augment the radio signals 54and/or 56.

FIG. 3A is a block diagram of the server 52A. The server 52A includes aradio transceiver 62, a virtual reference synthetic phase processor 63and an anomaly detector 63A. The server 52A receives data for thereference positions (or it already has the reference positions) and thereference phases from the reference stations 51A-N. The processor 63uses a virtual reference system (VRS) parametric model with the mastersynthetic vector 64 (in place of the virtual vector 27) together withthe master and auxiliary reference network positions and phases for thereference network stations 51A-N and the three dimensional angles to theGPS satellites 16 for inferring the synthetic reference phases thatwould be measured if the measurements were made at the syntheticposition 133 (instead of the virtual reference position 26).

The radio transceiver 62 transmits the radio signal 56 havingsynthesized reference data to the rover station 124A. The synthesizedreference data still includes a correct geographical virtual referenceposition 26, as is conventional, but includes the synthetic referencephases in place of the actual or virtual reference phases that are usedby a conventional rover station for positioning operation without theaccuracy control of the present invention.

FIG. 3B is a block diagram of the server 52B. The server 52B includesthe radio transceiver 62, a synthetic phase processor 65, a virtualreference processor 66 and an anomaly detector 66A. The server 52Breceives data for the reference positions (or it already has thereference positions) and the reference phases from the referencestations 51A-N. The virtual reference processor 66 uses the virtualvector 27 and the reference positions and phases for the referencestations 51A-N with the three dimensional angles to the GPS satellites16 for determining the virtual reference phases. The virtual referenceprocessor 66 then passes the virtual reference phases and the virtualreference position 26 to the synthetic phase processor 65.

The synthetic phase processor 65 uses the synthetic offset vector 32with the virtual reference phases and the three dimensional angles tothe GPS satellites 16 for inferring the synthetic reference phases forthe carrier phases that would be measured if the measurements were madeat the synthetic position 133. The radio transceiver 62 transmits theradio signal 56 having synthesized reference data to the rover station124B. The synthesized reference data still includes a correctgeographical virtual reference position 26, as is conventional, but thephases for the GPS signals 14 are not the virtual reference phases thatwould be measured at the virtual reference position 26 but are insteadsynthetic reference phases that would be measured at the syntheticposition 133.

FIG. 3C is a block diagram of the server 52C. The synthetic phaseprocessor 65 is located separately from the virtual reference processor66. The server 52C uses the public switch telephone network (PTSN)telephone system 68 for receiving reference data and uses the telephonesystem 68 for communication between the virtual reference processor 66and the synthetic phase processor 65. The processor 65 receives data forthe virtual reference position 26 and virtual reference phases from thevirtual reference processor 66 and then infers the synthetic referencephases as described above. The processor 65 may be located adjacent tothe rover station 124C having a local wired connection or a cellulartelephone 69 may be used to pass the synthetic reference phases to therover station 124C.

The virtual reference processors 63 and 66 determine double differencephase residuals between the master and auxiliary phases for current andprevious phase measurements and pass the phase residuals to therespective anomaly detectors 63A and 66A. The anomaly detector 63A and66A detects a phase residual anomaly when the phase residual is greaterthan a phase threshold corresponding to a selected distance or integritylimit 40 for RTK operation. The virtual reference processors 63 and theanomaly detectors 63A and 66A, respectively, may share hardware andsoftware.

The rover GPS receivers 125A-C also determine double difference phaseresiduals. The phase residuals determined in the rover GPS receivers arethe differences between the rover phases and the synthetic referencephases for current and previous phase measurements. The rover GPSreceivers 125A-C pass the phase residuals to the respective anomalydetectors 126A-C. The anomaly detectors 126A-C also detect a phaseresidual anomaly when the phase residual is greater than a phasethreshold corresponding to a selected distance or integrity limit 40 forRTK operation. The rover GPS receiver 125A-C and the anomaly detector126A-C, respectively, may share hardware and software.

The integrity limit 40 corresponds to a zone about the rover position38. When an anomaly is detected, the anomaly detector 63A, 66A or 126A-Cinhibits the rover GPS receiver 125A-C from providing the rover position38 to the user of the rover station 124A-C, or provides a notice to theuser that the anomaly was detected and allows the user to decide whetheror not to use the position 38. Alternatively, the rover station 124A-Cprovides a solution for the rover position 38 where the syntheticreference phase and measured rover phase for the particular GPS signal14 associated with the anomaly are not used. The effect of the system 50is that the rover position 38 has the controlled added position error 39without degrading the integrity limit 40 of the RTK positioning solutionfor the rover position 38.

In the system 50, it may be beneficial to reduce the amount of data thatis transmitted among various locations by sending differences betweenmaster and auxiliary reference network positions and/or referencenetwork phases in place of the actual reference positions and phases.For example, the reference positions and phases for the auxiliarystations 51B-N may be transmitted as differences with respect to thereference position and phases the master reference station 51A.

FIG. 4 is a diagram showing a secure real time kinematic (RTK) GPS roverstation 70 for receiving conventional reference data in a secure formatfrom a GPS-based positioning system 71. The positioning system 71includes at least one reference station 112 having a reference positionthat is established by a survey or some other means for receiving GPSsignals 14 from GPS satellites 16. The reference station 112 measuresthe carrier phases of the GPS signals 14 and sends a radio signal 117having secure reference data for the reference phases to the roverstation 70. The security of the reference data may be maintained by themeasures of the Digital Millennium Copyright Act of 1998 for preventingunauthorized access to a copyrighted work. Alternatively, the referencedata may be encrypted.

The rover station 70 receives or generates or otherwise selects thesynthetic offset vector 32. The synthetic offset vector 32 and thereference position of the reference station 112 define a syntheticposition 33 as described above. The length and direction of thesynthetic offset vector 32 is arbitrary but the length is normally a fewmeters or less. When it is desired for the rover station 70 to operatewith existing RTK GPS-based reference systems, the reference station 112may be a conventional reference station 12 described above with theaddition of security measures for protecting the reference data fromunauthorized access.

FIG. 4A is a block diagram of the rover station 70. The rover station 70includes an RTK rover GPS receiver 74 including an anomaly detector 74A,a secure synthetic phase processor 75, and a radio transceiver 76. Therover GPS receiver 74 measures the carrier phases for the same GPSsignals 14 that are measured by the reference station 112. The radiotransceiver 76 may be replaced by a radio receiver without a transmitterif two-way communication is not required. A cellular telephone may beused for the radio transceiver 76. The radio transceiver 76 receives thereference position and the secure reference data for the referencephases in the radio signal 117.

The secure synthetic phase processor 75 selects the synthetic offsetvector 32 and then uses the synthetic offset vector 32 with thereference position, the secure reference phases and the threedimensional angles to the GPS satellites for inferring the syntheticreference phases. The secure synthetic phase processor 75 performsprocessing on signals and data within physical boundaries of theprocessor 75 in a way that makes it difficult for an authorized user toalter the processing algorithms or view the signals or data. Further,the algorithms, signals, messages and data are protected by the accesscontrols of the Digital Millennium Copyright Act of 1998.

The secure synthetic phase processor 75 passes the synthetic referencephases to the rover GPS receiver 74. The GPS receiver 74 uses thesynthetic reference phases and the measured rover phases with thereference position and the three dimensional angles to the GPSsatellites 16 to compute the rover position 38. The conventional roverstation 18 would calculate the difference between the reference androver phase measurements for the distance vectors represented by thevector d to the GPS satellite 16A. However, the rover station 70 arrivesat estimated perpendicular distance vectors represented by d* instead ofthe vectors represented by d.

When the rover station 70 calculates its position with respect to thereference station 112, it arrives at a position 38 that has a vectorposition offset error 39 of equal length and in the opposite directionas the synthetic offset vector 32. The security measures in the secureprocessor 75 prevent the user from undoing the accuracy control of thepresent invention by using the measured reference phases instead of thesynthetic reference phases. Measurements by the rover GPS receiver 74from several GPS satellites 16 yield several perpendicular distancevectors d* and ultimately the position of the rover station 70 withrespect to the reference station 112 with the added error 39. Using thistechnique the secure synthetic phase processor 75 is able to introducethe arbitrary added error 39 into the position 38 that is calculated bythe rover station 70.

The rover GPS receiver 74 determines phase residuals from current andprevious synthetic reference phases and measured rover phases and passesthe phase residuals to the anomaly detector 74A. The anomaly detector74A detects a phase residual anomaly when the phase residual is greaterthan a phase threshold corresponding to a selected integrity limit 40for RTK operation. The integrity limit 40 corresponds to a zone aboutthe rover position 38. When an anomaly is detected, the anomaly detector74A inhibits the rover GPS receiver 74 from providing the rover position38 to the user of the rover station 70, or provides a notification tothe user that the anomaly was detected and allows the user to decidewhether or not to use the position 38. Alternatively, the anomalydetector 74A provides a solution for the rover position 38 where thesynthetic reference phase and measured rover phase for the particularGPS signal 14 associated with the anomaly are not used. The effect ofthe system 70 is that the rover position 38 has the controlled addedposition error 39 without degrading the integrity limit 40 of the RTKpositioning solution for rover position 38.

FIG. 5 is a diagram showing a secure real time kinematic (RTK) GPS roverstation 80A or 80B for receiving conventional reference data in a secureformat from a network positioning system 81. The rover station 80A-Breceives reference data having secure reference phases from the system81 and selects the synthetic offset vector 32 for controlling thepositioning accuracy that it provides. The security of the referencephases may be protected by the access control measures of the DigitalMillennium Copyright Act of 1998 and/or by encryption. The positioningsystem 81 includes a server 123 and a network of reference networkstations, referred to as 112A, 112B through 112N, having referencepositions that are known from a survey or other means.

The reference network stations 112A-N include reference GPS receiversfor receiving the GPS signals 14 from the GPS satellites 16 andmeasuring carrier phases. When it is desired for the rover station 80A-Bto operate with existing RTK GPS-based reference systems, the referencestations 112A-N may be conventional reference stations 12A-N and theserver 123 may be the conventional serve 23 described above with theaddition of security measures for protecting the reference data. One ofthe reference stations, illustrated as 112A, may be designated as amaster reference station and the other reference network stations 112B-Nas auxiliaries.

The reference network stations 112A-N communicate with the server 123 insignals 122 and the server communicates with the rover station 80A-Bwith a radio signal 127 having a secure data format so that thereference phases cannot easily be used by an unauthorized user. The sumof the virtual vector 27 and the synthetic offset vector 32 is a mastersynthetic vector 64. The position of the master reference station 112Aand the master synthetic vector 64 define a synthetic position 133.

FIG. 5A is a block diagram of the rover station 80A. The rover station80A includes a radio transceiver 82, a secure virtual referencesynthetic phase processor 83 and an RTK rover GPS receiver 84A includingan anomaly detector 86A. The radio transceiver 82 receives data for themaster and auxiliary reference positions and phases for the master andauxiliary reference network stations 112A-N in the radio signal 127. Theradio transceiver 82 may be a radio receiver without a transmitter iftwo-way communication is not required. The radio transceiver 82 may be acellular telephone. In order to reduce the amount of data that istransmitted, the reference positions and phases for the auxiliaryreference stations 112B-N may be transmitted as differences from thereference position and phases of the master reference station 112A.

The synthetic phase processor 83 receives or generates or otherwiseselects the synthetic offset vector 32 and then determines the virtualreference position 26, or negotiates with the server 123 to determinethe virtual reference position 26. The virtual reference position 26 andthe synthetic offset vector 32 define the synthetic position 133 wherethe synthetic position 133 is separated from the virtual referenceposition 26 by the synthetic offset vector 32. The processor 83determines the master synthetic vector 64 from the vector sum of thevirtual vector 27 and the synthetic offset vector 32 (or the virtualreference position 26 and the synthetic offset vector 32). The lengthand direction of the synthetic offset vector 32 are arbitrary but thelength is normally a few meters or less.

The processor 83 then uses the master synthetic vector 64, in place ofthe virtual vector 27, together with the master and auxiliary referencenetwork positions and phases for the reference network stations 112A-Nand the three dimensional angles to the GPS satellites 16 for inferringthe synthetic reference phases that would be measured if themeasurements were made at the synthetic position 133. The processor 83passes the synthetic reference data for the virtual reference position26 and the synthetic reference phases to the rover GPS receiver 84A. Therover GPS receiver 84A measures the phases of the same GPS signals anduses the measured rover phases, the master and auxiliary referencepositions and phases with the synthetic reference phases and the virtualreference position 26 for determining the rover position 38.

FIG. 5B is a block diagram of the rover station 80B. The rover station80B is similar to the rover station 70 described above with theexception that the rover station 80B uses the virtual reference position26 in place of the actual reference position of the reference station112. The rover station 80B includes a radio transceiver 82, the roverGPS receiver 84B including an anomaly detector 86B, and a securesynthetic phase processor 85. The radio transceiver 82 receives data forthe virtual reference position 26 and the virtual reference phases inthe radio signal 127.

The processor 85 uses the synthetic offset vector 32 (or the differencebetween the virtual reference position 26 and the synthetic position133) with the virtual reference position 26, virtual reference phasesand the three dimensional angles to the GPS satellites for inferring thesynthetic reference phases that would be measured at the syntheticposition 133. The processor 85 passes the synthetic reference data forthe virtual reference position 26 and the synthetic reference phases tothe rover GPS receiver 84B. The rover GPS receiver 84B measures thephases of the same GPS signals and uses the measured rover phases withthe synthetic reference phases and the virtual reference position 26 fordetermining the rover position 38.

The rover GPS receiver 84A-B determines phase residuals from current andprevious synthetic reference phases and measured rover phases and passesthe phase residuals to the anomaly detector 86A-B. The anomaly detector86A-B detects a phase residual anomaly when the phase residual isgreater than a phase threshold corresponding to a selected distance orintegrity limit 40 for RTK operation. The integrity limit 40 correspondsto a zone about the rover position 38. When an anomaly is detected, theanomaly detector 86A-B inhibits the rover GPS receiver 84A-B fromproviding the rover position 38 to the user of the rover station 80A-B,or provides a notification to the user that the anomaly was detected andallows the user to decide whether or not to use the position 38.Alternatively, the anomaly detector 86A-B provides a solution for therover position 38 where the synthetic reference phase and measured roverphase for the particular GPS signal 14 associated with the anomaly arenot used.

The position 38 calculated by the rover station 80A-B relative to thevirtual reference position 26 has the added positional offset error 39that is equal in length and in the opposite direction as the syntheticoffset vector 32. Using this technique the rover station 80A-B is ableto arbitrarily introduce the added error 39 into the position 38 withoutdegrading the integrity limit 40 of the RTK positioning solution for therover position 38.

The secure synthetic phase processors 83 and 85 perform processing onsignals and data that are embedded with the boundaries of the roverstations 80A and 80B in a way that makes it physically difficult forusers of the rover stations 80A and 80B to alter the processingalgorithms or view the signals or data. Further, the algorithms,signals, messages and data are protected by the access controls of theDigital Millennium Copyright Act of 1998.

FIGS. 6A and 6B are block diagrams of random reference generatorsreferred to by reference numbers 90A and 90B, respectively. The randomreference generator 90A is used in the synthetic phase processors 63 and83 with a VRS parametric model for generating synthetic referencephases. The random reference generator 90B is used in the syntheticphase processors 35, 65, 75 and 85 with an actual or virtual referenceposition for generating synthetic reference phases. The syntheticreference phases are passed from the systems 30 and 50 to the RTK GPSreceivers in the rover stations 118 or 124A-C for determining the roverposition 38; or computed in secure processors within the rover station70 or 80A-B for determining the rover position 38.

The random reference generators 90A and 90B include a random processvector generator 170. The random process vector generator 170 stores orreceives values for a maximum rate of change and one or more maximumdimensions and uses the values as inputs to a random or pseudo-randomprocess for continuously computing synthetic offset vectors 32.Importantly, because the synthetic offset vectors 32 are computed with arandom or nearly random process, the added error 39 is not easilyreversible by users or software programming in the rover stations.

The value or values for maximum dimensions may be a maximum radius forproviding a spherical error zone, a maximum radius and a maximum lengthfor providing a cylindrical error zone, three maximum lengths X, Y and Zfor providing a box error zone, or the like. The error zones refer to avolume or a three dimensional range of the added error 39 for the roverposition 38 about the position for the rover station that would bedetermined by an RTK rover station without accuracy control. Forexample, the added offset 39 for the box error zone has possible errorsx, y and z in three dimensions of |x|≦X, |Y|≦Y and |z|≦Z. The box errorzone need not have equal or orthogonal dimensions. The values for themaximum dimensions z=0 or x and y=0 may be used to constrain the randomprocess vector generator 170 so that the added error 39 is confined tohorizontal or vertical directions, respectively.

The added error 39 may be of relatively large magnitude but low rate ofchange in any direction while the rover GPS receiver, constructed forfixed RTK operation, continues to use the resolved integer number ofcarrier phase cycles for its positioning. By continuing to use theintegers, the rover position 38 has the integrity of the RTK GPSsolution within the integrity limit 40 as small as a few centimeterseven when the added error 39 is a few meters or more. The RTK roverposition 38 has high integrity even when the accuracy is degraded withthe present invention because the errors due to multipath are largelyeliminated. It will be appreciated by those skilled in the art thatmerely dithering the reference carrier phase measurements directly andproviding the dithered reference phases to the rover station may make itimpossible for an RTK rover station to resolve the carrier phaseinteger, thereby losing the benefit of the high integrity of the RTKposition solution.

The random reference generator 90A includes a vector summer 172 and avirtual reference phase synthesizer 174. The vector summer 172 sums thesynthetic offset vector 32 with the virtual vector 27 for determiningthe master synthetic vector 64. The virtual reference phase synthesizer174 uses the master synthetic vector 64 with the three dimensionalangles to the GPS satellites 16, and the master and auxiliary referencepositions and corresponding measured master and auxiliary referencecarrier phases for the GPS signals 14 for computing the syntheticreference phases. The synthetic reference phases are then used asdescribed above with the carrier phases measured by the RTK rover GPSreceiver for computing the rover position 38.

The random reference generator 90B includes a phase synthesizer 175. Thephase synthesizer 175 uses the synthetic offset vector 32 from therandom process vector generator 170 with a reference carrier phase andthe three dimensional angles to the GPS satellites 16 to compute thesynthetic reference phases for the GPS signals 14. The reference carrierphase may be an actual reference phase measured at an actual referenceposition or a virtual reference phase computed for the virtual referenceposition 26. The synthetic reference phases are then used as describedabove with the carrier phases measured by the RTK rover GPS receiver forcomputing the rover position 38.

FIG. 7 is a system diagram showing a secure real time kinematic (RTK)GPS rover station 200A or 200B for operation with a reference station212A or 212B, respectively, in a positioning system 201. The roverstation 200A-B receives reference system data in a secure form from thesystem 201 and receives or generates a synthetic offset vector 232 withrespect to the position of the reference station 212A-B. The securereference data is used in the rover station 200A-B for computing asecure position 210. The rover station 200A-B then dithers the secureposition 210 with the synthetic offset vector 232 to provide anunsecured rover position 238 having an added position error 239 to auser of the rover station 200A-B.

The vector for the added position error 239 is the same length anddirection as the synthetic offset vector 232. Double difference phaseresiduals are monitored in the rover stations 200A-B for maintaining anintegrity limit 240 for RTK operation about the secure position 210. Theintegrity limit 240 is an outer limit of a zone about the secureposition 210. The added position error 239 offsets the secure position210 to the unsecure position 238 without degrading the integrity limit240 about the unsecure position 238. The integrity limit 240 may betwenty centimeters or less. The length and direction of the syntheticoffset vector 232 and the added position error 239 are arbitrary but thelength is normally a few meters or less.

The reference station 212A-B has a reference position that isestablished by a survey or some other means for receiving GPS signals 14from GPS satellites 16 and measuring reference carrier phases. Thesynthetic offset vector 232 and the reference position define asynthetic position 233 of the reference station 212A-B. The referencestation 212A-B sends a radio signal 217 having the secure reference datafor the measured reference phases and the reference position to therover station 200A-B. Information for the synthetic offset vector 232may be included in the secure reference data transmitted to the roverstation 200A or generated within the rover station 200B or received inthe rover station 200A from some other secure source. When it is desiredfor the rover station 200B to operate with existing RTK GPS-basedreference systems, the reference station 212B may be a conventionalreference station 12 described above with the addition of security forthe reference data that is transmitted to the rover station 200B.

FIG. 7A is a block diagram of an embodiment for the reference station212A and the rover station 200A where the reference station 212Agenerates the synthetic offset vector 232. The reference station 212Aincludes a reference GPS receiver 252, a reference position memory 254,a synthetic vector generator 260, a secure reference data provider 262and a radio transducer 264. The reference GPS receiver 252 receives andmeasures the carrier phases for the GPS signals 14. The referenceposition memory 254 stores the position of the reference station 212A.The synthetic vector generator 260 generates the synthetic offset vector232. The secure data provider 262 processes the reference phases,reference position, and the synthetic offset vector 232 into a secureformat for the reference data. The radio transceiver 264 issues thesecure reference data in the radio signal 217 to the rover station 200A.

The rover station 200A includes a radio transceiver 272, an RTK roverGPS receiver 274 including an anomaly detector 275, and a positiondither processor 277. The radio transceiver 272 may be replaced by aradio receiver without a transmitter if two-way communication is notrequired. A cellular telephone may be used for the radio transceiver272.

The radio transceiver 272 receives the secure reference data for thesynthetic offset vector 232 and a reference position and measuredreference phases in the radio signal 217; and passes the referenceposition and phases to the GPS receiver 274 and the synthetic offsetvector 232 to the position dither processor 277. The GPS receiver 274measures the carrier phases for the GPS signals 14 for the same GPSsatellites 16 and calculates the differences between the reference androver phase measurements. The phase differences result in estimatedperpendicular distance vectors represented by the vector d for the GPSsignal 14A as described above for determining the secure rover position210.

The position dither processor 277 dithers the secure rover position 210with the synthetic offset vector 232 to provide the rover position 238having the added position error 239. Preferably, the position ditherprocessor 277 is a coded algorithm embedded in memory or signalprocessing hardware that is read or otherwise processed by the hardwareand software in rover GPS receiver 274. Both the rover GPS receiver 274and the position dither processor 277 must be secure from tampering byusers of the rover station 200A in order to prevent users from undoingthe accuracy control that is provided by the rover station 200A.

The rover GPS receiver 274 determines double difference phase residualsfrom current and previous reference phases and current and previousmeasured rover phases and passes the phase residuals to the anomalydetector 275. The anomaly detector 275 detects a phase residual anomalywhen the phase residual is greater than a phase threshold correspondingto a selected distance for the integrity limit 240. The integrity zoneabout the secure position 210 is transferred by the position ditherprocessor 277 to the integrity zone 240 about the dithered roverposition 238. When an anomaly is detected, the anomaly detector 275inhibits the position dither processor 277 from providing the roverposition 238 to the user of the rover station 200, or provides anotification to the user that the anomaly was detected and allows theuser to decide whether or not to use the position 238. Alternatively,the anomaly detector 275 provides a solution for the secure position 210and the position dither processor 277 provides the rover position 238where the reference phase and measured rover phase for the particularGPS signal 14 associated with the anomaly are not used.

FIG. 7B is a block diagram of an embodiment for the reference station212B and the rover station 200B where the rover station 200B generatesthe synthetic offset vector 232. The reference station 212B and therover station 200B operate as described above for the reference station212A and rover station 200A with the exception that the synthetic offsetvector 232 is generated by the synthetic vector generator 260 in therover station 200B.

FIG. 8 is a system diagram showing a secure real time kinematic (RTK)GPS rover station 300A, 300B, 300C or 300D for operation with a server323A, 323B, 323C or 323D, respectively, in a network positioning systemshown generally with a reference identifier 301. The rover station300A-D receives the secure reference system data from the system 301 andreceives or generates the synthetic offset vector 232 for controllingthe positioning accuracy that it provides. The synthetic offset vector232 offsets the virtual reference position 26 for the system 301 to asynthetic position 333. The reference data is used by the rover station300A-D for computing a secure position 310.

The rover station 300A-D then uses the synthetic offset vector 232 todither the secure position 310 to provide an unsecure rover position 338having the added position error 239 to a user of the rover station300A-D. The integrity limit 240 for RTK operation represents the outerlimit of a zone about the secure position 310. The added position error239 offsets the secure position 310 to the unsecure position 338 withoutdegrading the integrity limit 240 so that the integrity limit 240becomes the outer limit of a zone about the position 338. The vector forthe added position error 239 is the same length and direction as thesynthetic offset vector 232. The length and direction of the syntheticoffset vector 232 and the added position error 239 are arbitrary but thelength is normally a few meters or less.

The positioning system 301 includes a network of reference networkstations, referred to as 312A, 312B through 312N, having referencepositions that are known from a survey or other means. The referencestations 312A-N measure the carrier phases of the GPS signals 14 fromthe GPS satellites 16 and send telephone or radio signals 322 having thereference system data for the measured phases to the server 323A-D.Information for the synthetic offset vector 232 may be included in thesecure reference data transmitted to the rover station 300A,C orgenerated within the rover station 300B,D or received in the roverstation 300A,C from some other secure source. The server 323A-Dcommunicates with a radio signal 325 to send reference data in a secureformat to the rover station 300A-D. One of the reference stations,illustrated as 312A, may be designated as a master reference station andthe other reference network stations 312B-N as auxiliaries.

The system 301 determines the virtual reference position 26 and thevirtual vector 27 from the master reference station 312A to the virtualreference position 26. When it is desired for the rover station 300B,Dto operate with existing RTK GPS-based reference systems, the server323B,D and the reference stations 312A-N may be the server 23 and thereference stations 12A-N of the prior art with the addition of thesecurity for the reference data transmitted to the rover station 300B,D.It should be noted that the elements of the server 323A-D do not need tobe in one physical location.

FIG. 8A is a block diagram of an embodiment for the server 323A and therover station 300A where the server 323A generates the synthetic offsetvector 232. The server 323A includes the synthetic vector generator 260,a VRS position phase processor 352 including an anomaly detector 353, asecure reference data provider 354, and a radio transceiver 356. Thesynthetic vector generator 260 generates and passes the synthetic offsetvector 232 to the secure data provider 354.

The VRS reference position phase processor 352 receives the master andauxiliary reference phases from the reference stations 312A-N in thesignal 322. The master and auxiliary reference positions are retained bythe processor 352 or are received in the signal 322. The processor 352uses the virtual reference position 26 with the master and auxiliarypositions and phases from the reference stations 312A-N for determiningvirtual reference phases for the GPS signals 14 referred to the virtualreference position 26 and passes the reference data for the virtualreference position 26 and the virtual reference phases to the securedata provider 354. The anomaly detector 353 monitors double differencephase residuals between the current and previous measured phases betweenthe reference stations 312A-N for preventing the reference data frombeing used by the rover station 300A when one of the current referencephases is outside a phase residual threshold corresponding to theintegrity limit 240.

The secure data provider 354 processes the reference data into a secureformat and passes the secure reference data to the radio transceiver356. The radio transceiver 356 issues the secure reference data in theradio signal 325 to the rover station 300A. The rover station 300Aincludes the position dither processor 277, a radio transceiver 362, anda rover RTK GPS receiver 364 including an anomaly detector 365. Theradio transceiver 362 receives secure reference data in the radio signal325 and passes the reference system position and phase data to the roverGPS receiver 364 and the synthetic offset vector 232 to the positiondither processor 277. The radio transceiver 362 may be a radio receiverwithout a transmitter if two-way communication is not required. Theradio transceiver 362 may be a cellular telephone.

The rover GPS receiver 364 measures carrier phases for the GPS signals14 for the same GPS satellites 16 as the reference GPS receiver 352 andthen uses the reference system position and phase data for correctingthe carrier phases that it measures and ultimately arrives at the secureposition 310 with respect to the virtual reference position 26.

The rover GPS receiver 364 determines phase residuals from current andprevious reference phases and measured rover phases and passes the phaseresiduals to the anomaly detector 365. The anomaly detector 365 detectsa phase residual anomaly when the phase residual is greater than a phasethreshold corresponding to a selected integrity limit 240. The integritylimit 240 corresponds to a zone about the rover position 310. Theposition dither processor 277 dithers the secure position 310 with thesynthetic offset vector 232 for transferring the integrity limit 240 tothe unsecure position 338 having the added error 239. When an anomaly isdetected, the anomaly detector 365 inhibits the rover GPS receiver 364from providing the rover secure position 310 to the position ditherprocessor 277 and ultimately inhibits the rover station 300A fromproviding the rover position 338 to the user of the rover station 300A.Alternatively, the anomaly detector 365 provides the position 338 wherethe measured reference and rover phases for the particular GPS signal 14associated with the anomaly are not used.

FIG. 8B is a block diagram of an embodiment for the server 323B and therover station 300B where the rover station 300B generates the syntheticoffset vector 232. The server 323B includes the VRS position phaseprocessor 352 including the anomaly detector 353, the secure dataprovider 354, and the radio transceiver 356 as described above. Therover station 300B includes the synthetic vector generator 260, theposition dither processor 277, the radio transceiver 362, and the roverRTK GPS receiver 364 including the anomaly detector 365 as describedabove.

The radio transceiver 356 transmits the reference system data for thevirtual reference position 26 and the virtual reference phases in asecure format in the radio signal 325 to the rover station 300B. Thesynthetic vector generator 260 in the rover station 300B passes thesynthetic offset vector 232 to the position dither processor 277. Theposition dither processor 277 dithers the secure position 310 with thesynthetic offset vector 232 to provide the unsecure rover position 338having the integrity limit 240 to the user of the rover station 300B.

FIG. 8C is a block diagram of an embodiment for the server 323C and therover station 300C where the server 323C generates the synthetic offsetvector 232. The server 323C includes the synthetic vector generator 260,a reference server processor 368, the secure data provider 354, and theradio transceiver 356. The synthetic vector generator 260 generates andpasses the synthetic offset vector 232 to the secure data provider 354.

The reference server processor 368 receives the master and auxiliaryreference phases from the reference stations 312A-N in the signal 322.The master and auxiliary reference positions are retained by theprocessor 368 or are received in the signal 322. The processor 368passes the master and auxiliary reference positions and phases to thesecure data provider 354.

The secure data provider 354 processes the reference data into a secureformat and passes the secure reference data to the radio transceiver356. The radio transceiver 356 issues the secure reference data in theradio signal 325 to the rover station 300C. The rover station 300Cincludes the position dither processor 277, the radio transceiver 362,and a rover RTK GPS receiver 374 including an anomaly detector 375. Theradio transceiver 362 receives secure reference data in the radio signal325 and passes the reference system position and phase data to the roverGPS receiver 374 and the synthetic offset vector 232 to the positiondither processor 277. The radio transceiver 362 may be a radio receiverwithout a transmitter if two-way communication is not required. Theradio transceiver 362 may be a cellular telephone.

The rover GPS receiver 374 measures carrier phases for the GPS signals14 for the same GPS satellites 16 as the reference stations 312A-N andthen uses the reference system position and phase data for correctingthe carrier phases that it measures and ultimate arrives at the secureposition 310 with respect to the virtual reference position 26. Thesecure position 310 is passed to the position dither processor 277.

The rover GPS receiver 374 determines phase residuals from current andprevious reference phases and measured rover phases and passes the phaseresiduals to the anomaly detector 375. The anomaly detector 375 detectsa phase residual anomaly when the phase residual is greater than a phasethreshold corresponding to a selected integrity limit 240. The integritylimit 240 corresponds to the outer limit of a zone about the roverposition 310. The position dither processor 277 dithers the secureposition 310 with the synthetic offset vector 232 for transferring theintegrity limit 240 to the unsecure rover position 338 having the addedposition error 239 with respect to the virtual reference position 26.When an anomaly is detected, the anomaly detector 375 inhibits the roverGPS receiver 374 from providing the rover secure position 310 to theposition dither processor 277 and ultimately inhibits the rover station300C from providing the rover position 338 to the user of the roverstation 300C. Alternatively, the anomaly detector 375 provides asolution for the rover position 338 where the reference phase andmeasured rover phase for the particular GPS signal 14 associated withthe anomaly are not used.

FIG. 8D is a block diagram of an embodiment for the server 323D and therover station 300D where the rover station 300D generates the syntheticoffset vector 232. The server 323D includes the reference serverprocessor 368, the secure data provider 354, and the radio transceiver356 as described above. The rover station 300D includes the syntheticvector generator 260, the position dither processor 277, the radiotransceiver 362, and the rover RTK GPS receiver 374 including theanomaly detector 375, as described above.

The radio transceiver 356 transmits the reference system data for themaster and auxiliary reference positions and phases (or differencebetween the master and auxiliary positions and phases) in a secureformat in the radio signal 325 to the rover station 300D. The syntheticvector generator 260 in the rover station 300D generates and passes thesynthetic offset vector 232 to the position dither processor 277. Theposition dither processor 277 dithers the secure position 310 with thesynthetic offset vector 232 to provide the unsecure rover position 338to the user of the rover station 300D.

Using these techniques the secure rover station 200A-B,300A-D is able tointroduce the arbitrary added error 239 into the position 238,338 thatis provided by the rover station 200A-B,300A-D without degrading theintegrity limit 240 that is computed for the secure position 210,310.The reference data must be secure and both the rover GPS receiver274,364,374 and the position dither processor 277 must be secure fromtampering by users in order to prevent users from undoing the accuracycontrol that is provided by the rover station 200A-B,300A-D.

Anomaly detectors, such as 63A, 66A, 74A, 86A-B, 120, 126A-C, 275, 353,365 and 375, are described above for detecting anomalies (also known asoutliers) for phase residuals on a satellite-by-satellite basis for realtime kinematic (RTK) position determinations. The anomaly is detectedwhen the phase residual exceeds a selected phase residual limit. Thephase residual limit is selected so that when the phase residuals arewithin the phase residual limit, the position determination has thedesignated integrity limit 40,240.

The algorithms, signals, messages and data in the rover GPS receiver274,364,374, the position dither processor 277, and the reference datain the signals 127, 217 and 325 are provided with the access controlmeasures of the Digital Millennium Copyright Act of 1998. The referencedata in the signals 127, 217 and 325 may also be protected byencryption. The rovers 200A-B and 300A-D perform processing on signalsand data that are embedded with the boundaries of the rovers 200A-B and300A-D in a way that makes it mechanically or electrically difficult foran unauthorized user of the rovers 200A-B and 300A-D to alter thealgorithms or view the signals or data. All users are unauthorized usersunless they are designated by the provider of the algorithms, signals ordata as authorized users.

It may be noted that the positioning system 30, 50, 71, 81, 201 or 301could be used as the basis for a fee-based RTK GPS service wherein theprice for the service is based upon the accuracy of the positioning.

FIG. 9 is a block diagram illustrating the synthetic vector generator260 and the position dither processor 277. The synthetic vectorgenerator 260 includes a random process vector generator 380. The randomprocess vector generator 380 stores or receives values for a maximumrate of change and one or more maximum dimensions and uses the values asinputs to a random or pseudo-random process for continuously computingthe synthetic offset vector 232. The position dither processor 277includes a summer 382 for summing the synthetic offset vector 232 withthe secure position 210, 310. Importantly, because the synthetic offsetvector 232 is the same as the added positional error 239 and thesynthetic offset vector 232 is computed with a random or nearly randomprocess, the added positional error 239 is not easily reversible byunauthorized users.

The value or values for maximum dimensions may be a maximum radius valuefor providing a spherical error zone, a maximum radius and a maximumlength for providing a cylindrical error zone, three maximum lengths X,Y and Z for providing a box error zone, or the like. The error zonesrefer to a volume or a three dimensional range of the added positionerror 239 for the dithered (unsecure) rover position 238,338 about thesecure rover position 210,310. For example, the added error positionalerror 239 for the box error zone has possible errors x, y and z in threedimensions of |x|≦X, |Y|≦Y and |z|≦Z. The box error zone need not haveequal or orthogonal dimensions. The values for the maximum dimensionsz=0 or x and y=0 may be used to constrain the random process vectorgenerator 380 so that the added position error 239 is confined tohorizontal or vertical directions, respectively.

The added error 239 may be of relatively large magnitude in anydirection while the rover GPS receiver, constructed for fixed RTKoperation, continues to use the resolved integer number of carrier phasecycles for its positioning. By continuing to resolve the integers, therover position 238,338 has the integrity of the RTK GPS solution withinthe integrity limit 240 as small as a few centimeters even when theadded error 239 is a few meters or more. The RTK rover position 238,338has high integrity when the accuracy is degraded because the errors dueto multipath are largely eliminated. It will be appreciated by thoseskilled in the art that merely dithering the reference position directlyand providing the dithered reference position to the rover could make itimpossible for an RTK rover station to resolve the carrier phaseinteger, thereby losing the benefit of the high integrity of the RTKposition solution.

FIG. 10 is a flow chart of steps of a method for providing the syntheticreference phases from the reference system 30 having one referencestation to one or more rover stations. The steps may be embodied in atangible medium 600 containing instructions that may be read by aprocessor or processors for causing the system to carry out the steps.The medium 600 may be constructed with one or more memory devices suchas compact disks, electronic memory chips, hard disks, digital videodevices, or the like. The processor may be a device commonly known as acomputer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin a step 602. In a step 604, GPS signals are received at the referencestation by a real time kinematic (RTK) GPS receiver. In a step 606 thereference GPS receiver measures carrier phases of the GPS signals at areference position.

A synthetic position is defined by the reference position and thesynthetic offset vector. In a step 608 the reference system uses thesynthetic offset vector and the measured reference phases fordetermining synthetic reference phases for the GPS signals that would bereceived at the synthetic position. In a step 612 the reference systemtransmits synthesized reference data that includes the syntheticreference phases to the rover station.

A GPS rover station having an RTK GPS receiver receives the synthesizedreference data in a step 614. In a step 616 the rover GPS receiverreceives the GPS signals from the same GPS satellites. In a step 618 therover GPS receiver measures the carrier phases of the same GPS signals.In a step 622, the synthetic reference phases and the measured roverphases are used for testing the integrity of the phase measurements. Ina step 624, when integrity has been verified, the rover station uses thereference position, the synthetic reference phases and the rover phasesfor determining its position. The position that is determined by therover station has the same RTK integrity as if it were determined withthe phases for the reference position but with an added offset error,unknown to the rover station, equal in length to the synthetic offsetvector.

FIG. 11 is a flow chart of steps of a method for providing the syntheticreference phases from a reference network system, such as the referencenetwork system 50, to one or more rover stations. The steps may beembodied in a tangible medium 650 containing instructions that may beread by a processor or processors for causing the system to carry outthe steps. The medium 650 may be constructed with one or more memorydevices such as compact disks, electronic memory chips, hard disks,digital video devices, or the like. The processor may be a devicecommonly known as a computer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin the step 602. In a step 652 one of the network of reference stationsis designated as the master reference station. In a step 654 GPS signalsare received at the reference network stations. In a step 656 the realtime kinematic (RTK) GPS receivers at the reference stations measurereference network phases for the carriers of the GPS signals atreference network positions.

A virtual reference position is selected by the system or negotiatedbetween the system and the rover station in a step 662. In a step 664 avirtual vector is calculated between the position of the masterreference station and the virtual reference position. In a step 666 amaster synthetic vector is calculated by adding the virtual vector andthe synthetic offset vector. A synthetic position is defined by thevirtual reference position and the synthetic offset vector orequivalently by the position of the master reference station and themaster synthetic vector. In a step 674 the system uses the mastersynthetic vector, the reference network positions and the measuredreference network phases for mathematically determining the syntheticreference phases that would be measured for GPS signals received at thesynthetic position. In a step 675 the reference system uses doubledifference phase residuals of the master and auxiliary reference phasesfor testing integrity. In a step 676 when the integrity of the referencephases has been determined, the system transmits synthesized referencedata including the synthetic reference phases. In a step 678 the roverstation receives the synthetic reference data.

A GPS rover station having a real time kinematic (RTK) GPS receiverreceives the GPS signals from the same GPS satellites in a step 682. Ina step 684 the rover GPS receiver measures the carrier phases of the GPSsignals. In a step 685, the synthetic reference phases and the measuredrover phases are used for testing the integrity of the phasemeasurements. In a step 686, when integrity has been verified, the roverstation uses the synthetic reference phases for determining itsposition. The accuracy of the position that is determined by the roverstation has the same integrity as if it were determined in an RTKsolution with the phases for virtual reference position but with anadded offset error, unknown to the rover station, equal in length to thesynthetic offset vector.

FIG. 12 is a flow chart of steps of a method for computing syntheticreference phases in a rover station, such as the rover station 70, andthen using the synthetic reference phases for computing a rover positionhaving an added error. The steps may be embodied in a tangible medium700 containing instructions that may be read by a processor orprocessors for causing the rover station to carry out the steps. Themedium 700 may be constructed with one or more memory devices such ascompact disks, electronic memory chips, hard disks, digital videodevices, or the like. The processor may be a device commonly known as acomputer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin a secure synthetic phase processor in the rover station in a step702. In a step 704, GPS signals are received at a reference position bya real time kinematic (RTK) GPS receiver in a GPS reference station. Asynthetic position is defined by the reference position and thesynthetic offset vector. In a step 706 the reference GPS receivermeasures carrier phases of the GPS signals. In a step 708 the referencesystem transmits a signal having secure reference data that includes thereference position and measured reference phases.

The rover GPS receiver receives the secure reference data from thesystem in a step 714. In a step 716 the rover GPS receiver receives theGPS signals from the same GPS satellites. In a step 718 the rover GPSreceiver measures the carrier phases of the GPS signals. In a step 722the rover station uses the reference position and phases and thesynthetic offset vector for inferring the synthetic reference phases forthe GPS signals that would be received at the synthetic position. In astep 723, the synthetic reference phases and the measured rover phasesare used for testing the integrity of the phase measurements. In a step724, when integrity has been verified, the rover GPS receiver uses thereference position, the synthetic reference phases and the measuredrover phases for determining its position. The accuracy of the positionthat is determined by the rover station has the same RTK integrity as ifit were determined with the true reference phases but with an addedoffset error, unknown to the rover station, equal in length to thesynthetic offset vector.

FIG. 13 is a flow chart of steps of a method for computing syntheticreference phases in a rover station such as the rover station 80A or80B, and then using the synthetic reference phases for computing a roverposition having an added error. The steps may be embodied in a tangiblemedium 750 containing instructions that may be read by a processor orprocessors for causing the rover station to carry out the steps. Themedium 750 may be constructed with one or more memory devices such ascompact disks, electronic memory chips, hard disks, such as digitalvideo devices, or the like. The processor may be a device commonly knownas a computer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin a secure phase processor in the rover station in the step 702. In astep 752 one of a network of reference stations is selected ordesignated as the master reference station. In a step 754 GPS signalsare received by real time kinematic (RTK) GPS receivers at GPS referencenetwork stations. In a step 756 the reference GPS receivers measurereference network phases for the carriers of the GPS signals.

A virtual reference position is selected by the system or negotiatedbetween the system and the rover station in a step 762. In a step 764 avirtual vector is calculated from the position of the master referencestation to the virtual reference position. A synthetic position isdefined by the virtual reference position and the synthetic offsetvector. In a step 774 the system or the rover station computes virtualreference phases from the virtual reference vector and the referencenetwork positions and phases. In a step 776 the system transmits securereference data having the measured master and auxiliary referencepositions and phases or the virtual reference position and phases to therover station.

The rover GPS receiver receives the GPS signals from the same GPSsatellites in a step 778. In a step 782 the rover GPS receiver measuresthe carrier phases of the GPS signals. In a step 784 the rover stationuses the synthetic offset vector directly or indirectly through themaster synthetic vector (calculated by adding the virtual vector and thesynthetic offset vector), and the virtual reference position and phasesor the master and auxiliary positions and phases for computing thesynthetic reference phases for the synthetic position. In a step 785,the synthetic reference phases and the measured rover phases are usedfor testing the integrity of the phase measurements. In a step 786, whenintegrity has been verified, the rover GPS receiver uses the virtualreference position and phases and the synthetic reference phases fordetermining a position. The accuracy of the position that is determinedby the rover station has the same RTK integrity as if it were determinedfor the virtual reference phases but with an added offset error, unknownto the rover station, equal in length to the synthetic offset vector.

FIG. 14 is a flow chart of steps of a method for adding an error, shownand described above as the added error 239, to a rover position. Thesteps may be embodied in a tangible medium 800 containing instructionsthat may be read by a processor or processors for causing the roverstation to carry out the steps. The medium 800 may be constructed withone or more memory devices such as compact disks, electronic memorychips, hard disks, digital video devices, or the like. The processor maybe a device commonly known as a computer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin the rover station in a step 802. In a step 804, GPS signals arereceived at a reference position by a real time kinematic (RTK) GPSreceiver in a GPS reference station. In a step 806 the reference GPSreceiver measures carrier phases of the GPS signals. In a step 808 thereference system transmits secure reference data that includes thereference position and measured reference phases in a secure format tothe rover station.

The secure rover station receives the reference data in a step 814. Therover GPS receiver receives the GPS signals from the same GPS satellitesin a step 816. In a step 818 the rover GPS receiver measures the carrierphases of the same GPS signals. In a step 820, the reference and roverphases are tested for the integrity of the phase measurements. In a step822 the rover GPS receiver uses the reference data and the rover GPSphase measurements for determining a secure rover position. The secureposition is not made available to normal users of the rover station. Ina step 824 the rover station dithers the secure rover position with thesynthetic offset vector from the step 802 to provide an unsecure roverposition to users of the secure rover station. The unsecure roverposition has the added error equivalent to the synthetic positionoffset.

FIG. 15 is a flow chart of steps of a method for adding an error, shownand described above as the added error 239, to a rover position. Thesteps may be embodied in a tangible medium 850 containing instructionsthat may be read by a processor or processors for causing the roverstation to carry out the steps. The medium 850 may be constructed withone or more memory devices such as compact disks, electronic memorychips, hard disks, digital video devices, or the like. The processor maybe a device commonly known as a computer or a microprocessor.

A synthetic offset vector is received or generated or otherwise selectedin a secure rover station in the step 802. In a step 852 one of anetwork of reference stations is selected or designated as the masterreference station. In a step 854 GPS signals are received by real timekinematic (RTK) GPS receivers at GPS reference network stations. In astep 856 the reference GPS receivers measure reference network phasesfor the carriers of the GPS signals.

A virtual reference position is selected by the system or negotiatedbetween the system and the rover station in a step 862. In a step 864 avirtual vector is calculated from the position of the master referencestation to the virtual reference position. In a step 874 the system orrover computes virtual reference phases from the virtual referencevector and the reference network positions and phases. In a step 876 thesystem transmits reference data including the reference phases in asecure format to the rover station. In a step 877 the secure roverstation receives the reference data.

A GPS receiver in the rover station receives the GPS signals from thesame GPS satellites in a step 878. In a step 882 the rover GPS receivermeasures the carrier phases of the same GPS signals. In a step 883, thereference network and rover phases are tested for the integrity of thephase measurements. In a step 884 the rover GPS receiver uses thereference network and the rover GPS phase measurements for determining asecure rover position. The secure position is not made available tonormal users of the rover station. In a step 886 the rover stationdithers the secure rover position with the synthetic offset vector toprovide an unsecure rover position to users of the rover station. Theunsecure rover position has the added error that is equivalent to thesynthetic offset vector.

The reference data, rover stations, and structural parts of the roverstations are described in several embodiments of the invention assecure. In the context of the invention, the term “secure” means thatsecurity provisions have been made to inhibit or prevent unauthorizedusers from viewing, accessing or changing the signals, the data or thealgorithms in the secure elements. The security provisions may includeencryption, the privacy measures of the Digital Millennium Copyright Actof 1998 for preventing unauthorized access to a copyrighted work, andphysical constraints such as sealed packaging and using embedded codes,signals and data in ways so that it is physically or mechanicallydifficult view, access or change the codes, signals and data. A secureposition is only available to an authorized user. An unsecure positionis a position that is available to unauthorized (normal) users.

The provider of the reference system, the provider of the referencedata, and/or the provider of the algorithms for controlling thepositional accuracy of the rover station designate the parties that areauthorized users. All other users of the reference system, referencedata and/or rover stations are unauthorized users. Anyone not designatedby the provider for controlling the position accuracy is an“unauthorized user”. The unauthorized user is constrained from using therover station for obtaining a positional accuracy that does not have theadded positional error that is controlled by the provider. In generalthe provider is or represents the seller of the reference system, thereference data, or the rover station and the unauthorized user is theone who is using the rover station for field work as the normal user orend user for the rover positions.

The FIGS. 2 and 10 illustrate embodiments where a single referencestation system generates synthetic reference phases and provides thesynthetic reference phases in an unsecure (public) signal to an existingrover station. The FIGS. 3 and 11 illustrate embodiments where areference network system generates synthetic reference phases andprovides the synthetic reference phases in a public signal to anexisting rover station. The FIGS. 4 and 12 illustrate embodiments wherea secure rover station synthesizes synthetic reference phases from thetrue reference phases received in a secure (private) signal from asingle reference station system. The FIGS. 5 and 13 illustrateembodiments where a secure rover station synthesizes synthetic referencephases from the true reference phases received in a secure (private)signal from a reference network system.

The FIGS. 7 and 14 illustrate embodiments where a secure rover stationreceives reference data in a secure (private) signal from a singlereference station system, computes a secure private true position anddithers the secure position with a synthetic offset vector for providingan unsecure position to a user. The FIGS. 8 and 15 illustrateembodiments where a rover station receives reference data in a secure(private) signal from a reference network system, computes a true secureprivate position and dithers the secure position with a synthetic offsetvector for providing an unsecure position to a user.

FIG. 16 is a block diagram of a global navigation satellite system(GNSS) system 950 having real time kinematic (RTK) reference system 960,a rover receiver 970, and a computer apparatus 1000. The computerapparatus 1000 receives the GNSS RTK reference data including GNSSsatellite reference carrier phases from the reference system 960 througha communication path 965; and receives the GNSS RTK rover data includingGNSS satellite rover carrier phases from the rover receiver 970 througha communication path 975.

The path 965 may be the internet, a radio signal, or some other signalmedium or a tangible medium. The path 975 may be a tangible medium suchas a flash card, a docking of the rover receiver 970 to the computerapparatus 1000, or some other tangible medium or a signal medium. Thecomputer apparatus 1000 has a post-processing capability for determininga position 1010 (FIG. 17) of the rover receiver 970 that is kept securewithin the apparatus 1000 and a position 1038 (FIG. 17) that is madeavailable to a user of the apparatus 1000 where the user-availableposition 1038 has a selectable degraded accuracy or precision 1041 (FIG.17).

Typically the computer apparatus 1000 is located in a different placethan the rover receiver 970 and post processes the reference and roverdata at a later time than the GNSS signals are received for thedeterminations of the reference and rover carrier phases. Thegeographical positions of the rover receiver 970 and the computerapparatus 1000 are entirely unrelated. The later time for processing thedata is typically hours or days but possibly years. In a typicaloperation the rover receiver 970 has been moved to another site beforethe apparatus 1000 determines the secure rover position 1010. In anembodiment the computer apparatus 1000 is greater than 150 kilometersfrom the rover receiver 970 and the post processing is more than 12hours after the determinations of the reference and rover carrierphases.

FIG. 17 is a two dimension geographical position diagram representingthree dimension positions of the rover receiver 970 with respect to thereference system 960. A secure rover position 1010 is determined by acomputer apparatus 1000 having a centimeter level kinematicpost-processing (KPP) capability. The secure position 1010 has anintrinsic uncertainty referred to as an intrinsic accuracy or anintrinsic precision 1040 due to the GNSS satellites that are used tocompute the secure position 1010 and several other factors such assignal to noise ratios and/or estimated multipath errors of thesatellite signals. The secure position 1010 is analogous to the securepositions 210 (FIGS. 7, 7A-B and 9) and 310 (FIGS. 8, 8A-D and 9) andthe intrinsic precision 1040 is analogous to the integrity limits 40(FIGS. 2-5) and 240 (FIGS. 7-8) described above.

The user-available rover position 1038 is provided to a user with anadded error 1039 that degrades the intrinsic precision 1040. The streamof added errors 1039 have a standard deviation to provide theuser-available rover position 1038 at the selected precision 1041. Theadded errors 1039 are in general 3 dimensional vectors having varyingdirections and lengths. The user-available rover position 1038 isanalogous to the rover positions 38 (FIGS. 2, 3, 3A-C, 4, 4A, 5 and5A-B), 238 (FIGS. 7, 7A-B and 9), and 338 (FIGS. 8, 8A-D and 9) and theadded error 1039 is analogous to added errors 39 (FIGS. 2-5) and 239(FIGS. 7-8) described above.

The intrinsic precision 1040 and the selected precision 1041 are shownas circles having diameters representative of standard deviations. Inthe illustrated case, an instantaneous user-available rover position1038 is within the standard deviation of the selected precision 1041.The added error 1039 may sometimes place the user rover position 1038outside the standard deviation of the selected precision 1041.

FIG. 18 is a block diagram of the computer apparatus 1000 having aspecialized kinematic post-processing (KPP) capability. The computerapparatus 1000 may be a standard personal computer with the addition ofsoftware and/or hardware for a kinematic post-processor (KPP) 1102, avector offset generator 1104 and a position dither processor 1106. Thepost-processor 1102 receives RTK reference data including measurementsor determinations of GNSS reference carrier phases from the GNSS RTKreference system 960 and RTK rover data including measurements ordeterminations of GNSS rover carrier phases from the RTK rover receiver970.

The post-processor 1102 uses the RTK reference and rover data to computethe secure rover position 1010. The vector offset generator 1104generates offset vectors for providing the added errors 1039. Theposition dither processor 1106 adds the offset vectors to the secureposition 1010 to provide the user-available rover position 1038 havingthe selected precision 1041.

The post-processor 1102 includes a dilution of precision (DOP)calculator 1108 and an intrinsic precision estimator 1109. The DOPcalculator 1108 calculates the horizontal DOP (HDOP) and the verticalDOP (VDOP) for the geometry of the satellites that are used in thecalculation of the secure position 1010. The intrinsic precisionestimator 1109 estimates the intrinsic precision 1040 of the secureposition 1010. In an embodiment the intrinsic precision 1040 is computedwith a covariance matrix of the position fix for the secure position1010.

The vector offset generator 1104 includes an accuracy leveler 1112 and arandom process generator 1114. The accuracy leveler 1112 receivesinformation for the selected precision 1041 and uses the intrinsicprecision 1040 to compensate the selected precision 1041 to compute adither level. The compensation reduces or eliminates variation of theselected precision 1041 due to variation of the intrinsic precision1040. The effect of the compensation is to hold the selected precision1041 approximately constant and independent of the intrinsic precision1040 as long as the intrinsic precision 1040 is better than the selectedprecision 1041.

The random process generator 1114 generates a sequence for a stream ofoffset vectors having a standard deviation of the dither level that wascomputed by the accuracy leveler 1112. In an embodiment the randomprocess generator 1114 has east, north and up random processors 1114E,1114N and 1114U, respectively, for providing the east, north and up(vertical) components of the offset vectors. In an embodiment the randomprocess generator 1114 uses a selected settling time constant, aselected bias, and a seed for generating the sequence of offset vectors.The position dither processor 1106 adds the offset vectors to the securerover position 1010 to provide the user-available rover position 1038with the selected precision 1041 to the user.

FIG. 19 is a block diagram of the random process generator 1114 having aseed generator 1120, a bias generator 1121, a sequence generator 1122and an elongator 1124. The seed generator 1120 generates a seed value tobe associated with a particular set of GNSS RTK reference and rover datathat is received by the computer apparatus 1000 for a particular KPPposition fix. The bias generator 1121 generates a position error bias tobe associated with the particular data set.

The sequence generator 1122 uses the seed value to generate or select afirst pseudorandom sequence w(i) having a near Gaussian distribution. Inan embodiment the white noise w(i) sequence can be generated by firsttaking a uniformly distributed random number (C function-rand ( )),converting it to the range 0-1, then normalizing it via an approximationto the Error Function (see Abramovitz and Stegan, 1970, Handbook ofMathematical Functions, 9th edition, Dover, N.Y., for approximations tothe Error Function). This process is repeatable by seeding the rand( )function as this function is pseudorandom and generates the variableusing a known algorithm. Using the same seed each time results in thesame sequence of uniform value which in turn results in the samesequence of w(i). Finally, using the same w(i) then results in the sameg(i). In an embodiment the seed value is effectively the first 32 bitsas stored in the header of the file for GNSS reference and rover dataset.

By always using the same seed value, the sequence w(i) is repeatable sothat post-processing the same data set multiple times gives the sameuser-available rover position 1038. This is beneficial because otherwisea user would have possibly disconcerting results of seeing differentposition for the position 1038 each time the post processing wasperformed.

The elongator 1124 uses a selected time constant T with the sequencew(i) and the dither level a from the accuracy leveler 1112 and theselected bias error k₀ to generate a second (elongated) pseudorandomsequence g(i) for the offset vectors. The elongated sequence g(i) hasthe selected time constant T to provide a longer time to average to thebias error k₀, or to average to zero if the bias is zero, than the firstsequence w(i). The elongator 1124 passes the offset vectors to theposition dither processor 1106. The use of the mean bias error isbeneficial so that the user-available position 1038 is not averaged tothe secure position 1010 by running the post processing for a longertime.

Elongation Process

The process for elongating a pseudorandom sequence for degrading thesecure position 1010, which may be a KPP fixed solution, is via positioncoordinate dithering, i.e. applying pseudo random errors to thelatitude, longitude and height components of the rover position 1010. Afirst-order Gauss-Markov (GM) process may be used because the GM processproduces a distribution of errors that follow a normal distribution whenaveraged over time. The GM process can be controlled so that the errorschange slowly over time and therefore the dithering process would bedifficult to remove by the user as opposed to pure Gaussian errors ofthe first sequence w(i) which could be quickly averaged out.

An algorithm 1 shows a GM process for generating the elongated sequencefor the stream of offset vectors.

$\begin{matrix}{{g(i)} = {{{\mathbb{e}}^{(\frac{{- \Delta}\; t}{T})}{g\left( {i - 1} \right)}} + {{w(i)}\sigma\sqrt{\left( {1 - {\mathbb{e}}^{(\frac{{- 2}\;\Delta\; t}{T})}} \right)}}}} & (1)\end{matrix}$Where:

-   g(i) is the value of the GM process at epoch i.-   Δt time difference between samples.-   T correlation time of the GM process.-   w(i) white noise at epoch i which has a Normal distribution.-   e Euler's number.-   σ Dither level standard deviation.

The selected correlation time constant T of the GM process defines howquickly the dithering errors can be averaged out, while C defines themagnitude of the GM dithering errors. The GM dithering errors would takeroughly 3 times the time constant T to average out.

The white noise w(i) input can be generated by first taking a uniformlydistributed random number (C function-rand( )), converting it to therange 0-1, then normalizing it via an approximation. The dither processg(i) mean of the algorithm 1 approaches zero average for long timeperiods (more than about 3T). A post processing user could conceivablynegate this dither process with static data by processing his data setbut would need a sufficiently long time more than about 3T to do so.

An algorithm 1a shows a position error bias k₀ for generating a randomprocess dither sequence b₀(i) that may be used for providing thesequence of offset vectors.b ₀(i)=k ₀ +w(i)σ  (1a)Where:

-   b₀(i) is the value of the output process at epoch i.-   w(i) white noise at epoch i which has a Normal distribution.-   k₀ is a bias of the dither sequence g(i).-   σ Dither level standard deviation.

The dither process b₀(i) mean never averages to zero so it cannot benegated for any length of time. The bias k₀ may be a variable determinedrandomly for each data set. To avoid confusing a user the k₀ might belimited to small changes for small user edits of the data set.

An algorithm 1b shows a combination of the ideas of the GM process forgenerating an elongated sequence g(i) and the position bias error k₀ forgenerating the stream of offset vectors.

$\begin{matrix}{{g(i)} = {{{\mathbb{e}}^{(\frac{{- \Delta}\; t}{T})}{g\left( {i - 1} \right)}} + {k_{0}\left\lbrack {1 - {\mathbb{e}}^{({1 - \frac{\Delta\; t}{T}})}} \right\rbrack} + {{w(i)}\sigma\sqrt{\left( {1 - {\mathbb{e}}^{(\frac{{- 2}\;\Delta\; t}{T})}} \right)}}}} & \left( {1\; b} \right)\end{matrix}$Where:

-   g(i) is the value of the GM process at epoch i.-   Δt time difference between samples.-   T correlation time of the GM process.-   k₀ is a bias of the dither sequence g₀(i).-   w(i) white noise at epoch i which has a Normal distribution.-   e Euler's number.-   σ Dither level standard deviation.

The algorithm 1b shows a pseudorandom sequence g(i) computed with thebias error k₀ to provide a non zero average with a standard deviation σfor the computed dither level. The dither process g(i) mean for thealgorithm 1b approaches the bias k₀ for long time periods more thanabout 3T.

Standard Deviation Calculation for Dither

FIG. 20 is a block diagram of an embodiment of the position ditherprocessor 1106 and the vector offset generator 1104 where the vectoroffset generator 1104 includes the accuracy leveler 1112 and theelongator 1124. In this embodiment, covariance information for thesecure position 1010 is used to compensate the selected precision 1041with the intrinsic precision 1040 in order to decrease the lengths ofthe offset vectors as the intrinsic precision 1040 gets worse andincrease the lengths of the offset vectors as the intrinsic precision1040 gets better so that the selected precision 1041 that is provided tothe post processing user remains about the same even when the intrinsicprecision 1040 varies.

The accuracy leveler 1112 includes a horizontal precision compensator1132, a vertical precision compensator 1134, an east horizontal scaler1136, a north horizontal scaler 1138, and east, north and up square rootfunctions 1139, 1140 and 1141, respectively. The selected precision 1041may be composed of a selected horizontal precision (hzPrecInput) and aselected vertical precision (vtPrecInput). The horizontal and verticalprecisions may be selected independently. The accuracy leveler 1112receives information for the selected horizontal precision and theselected vertical precision respectively, and issues dither levels foreast, north and up.

The horizontal precision compensator 1132 compensates the level of thehzPrecInput with east and north covariance diagonal components Qee andQnn, respectively, to provide a compensated horizontal dither levelvariance (hzVarDither). Similarly, the vertical precision compensator1134 compensates the vtPrecInput with the up covariance diagonalcomponent Quu to provide a compensated vertical dither level variance(vtVarDither).

The east horizontal scaler 1136 uses the covariance components Qee andQnn to scale the hzVarDither to provide an east dither level variance(EastVarDither). Similarly, the north horizontal scaler 1138 uses thecovariance components Qee and Qnn to scale the hzVarDither to provide anorth dither level variance (NorthVarDither). The east, north and upsquare root functions 1139, 1140 and 1141 compute the square roots ofEastVarDither, NorthVarDither and vtVarDither, respectively, to providedither level standard deviations for east σ_(e), north σ_(n), and upσ_(u), respectively.

The elongator 1124 includes an east sequence elongator 1144E, a northsequence elongator 1144N, and a vertical sequence elongator 1144U. In anembodiment the epochs i of the sequence w(i) have epoch offsets toprovide an east sequence w(i_(e)), a north sequence w(i_(n)) and an upsequence w(i_(u)). Alternatively, three separate sequences w_(e)(i),w_(n)(i), and w_(u)(i) may be used for east, north and up, respectively.The east sequence elongator 1144E processes the east dither levelstandard deviation σ_(e) with the sequence w(i_(e)) to provide a streamof east offsets as an east elongated sequence g(i_(e)). Similarly, thenorth sequence elongator 1144N processes the north dither level standarddeviation σ_(n) with the sequence w(i_(n)) to provide a stream of northoffsets as a north elongated sequence g(i_(n)).

The vertical sequence elongator 1144U processes the up dither levelstandard deviation au with the sequence w(i_(u)) to provide a stream ofup offsets as an up elongated sequence g(i_(u)). In an embodiment, themean bias error vector components k_(0e), k_(0n) and k_(0u) are used bythe east, north and up sequence elongators 1144E, 1144N and 1144U,respectively, to bias the mean values of the g(i_(e)), g(i_(n)) andg(i_(u)) sequences. The steam of the complex combination of east, northand up offsets is the stream of the vector offsets that is passed to theposition dither processor 1106.

The position dither processor 1106 includes an east adder 1151, a northadder 1152 and an up adder 1153. The east, north and up adders 1151,1152 and 1153 add the east, north and up offsets to east, north and upcomponents, respectively, of the secure position 1010 to provide theeast, north and up components of the rover position 1038 that isavailable to a user.

The equations 2-8 show the computation of the east, north and up ditherlevels. Once the hzPrecInput and vtPrecInput (the horizontal andvertical selected precisions, respectively) are defined, it is necessaryto compute the level of position dither needed. The dither variancesshown in equations 2 and 3 are the differences between the actual(intrinsic) position variances achieved with a KPP position fix for thesecure position 1010 and the required (selected) position variances.hzVarDither=hzPrecInput*hzPrecInput−(Qee+Qnn)  (2)vtVarDither=vtPrecInput*vtprecInput−(Quu)  (3)

The Qee, Qnn, Quu are the diagonal components of the actual KPP positionfix covariance matrix (typically around 1.0e−4 m² for fixed-ambiguitysolutions). The hzVarDither, vtVarDither are the horizontal and verticalvariances of the dither needed to provide the selected precision 1041.If the kinematic post processing is only generating a float solution,then it is possible that hzPrecOutput² is less than the currenthorizontal position precision (Qee+Qnn), in which cause no error isadded.

The relative east/north dither level may be set based on the ratio ofthe east and north covariance elements in the position fix as shown inequations 4 and 5.scaleEastDither=Qee/(Qee+Qnn)  (4)scaleNorthDither=Qnn/(Qee+Qnn)  (5)

The east, north and up coordinates of each KPP position fix are ditheredseparately by east, north and up dithering processes. The dithering mayuse different east, north, up sequences (g_(e)(i), g_(n)(i), g_(u)(i))or the same sequence having different epoch offsets (g(i_(e)), g(i_(n)),g(i_(u))). The standard deviations used to generate the east, north andup dither processes are then computed according to equations 6, 7 and 8.σ_(e)=scaleEastDither×√{square root over (hzVarDither)}  (6)σ_(n)=scaleEastDither×√{square root over (hzVarDither)}  (7)σ_(u)=√{square root over (vtVarDither)}  (8)Using Satellite Geometry to Control Dither Level

An optional design of the dither process uses the prevailing satellitegeometry to set the level of dithering. The solution DOP provides anunweighted measure of the satellite geometry and therefore provides aninput that may be used to adapt the output statistics for the user roverposition 1038. In an embodiment, the acceptable range of positionaldilution of precision (PDOP) for KPP positioning is up to 7.0. In thiscase the selected precision 1041 would become worse as DOP increased andbetter as DOP decreased.

FIG. 21 is a block diagram of an optional dilution of precision (DOP)scaler 1160 that may be included in the vector offset generator 1104 touse satellite geometry to control degradation. The DOP computed by thepost processor 1102 (FIG. 18) for the secure position 1010 includes ahorizontal DOP (HDOP) and a vertical DOP (VDOP). The DOP scaler 1160includes a horizontal precision selector 1162 and a vertical precisionselector 1164. The horizontal precision selector 1162 determines thehorizontal selected precision by multiplying the HDOP by a selected HDOPscale factor and adding a selected HDOP offset to provide thehzPrecInput (FIG. 20). Similarly, the vertical precision scaler 1164determinants the vertical selected precision by multiplying the VDOP bya selected VDOP scale factor and adding a selected VDOP offset toprovide the vtPrecInput (FIG. 20).

The selected horizontal and vertical precisions are obtained viaequations 9 and 10.hzPrecInput=HDOP_SCALE_FACTOR*HDOP+HDOP_OFFSET  (9)vtPrecInput=VDOP_SCALE_FACTOR*VDOP+VDOP_OFFSET  (10)where HDOP and VDOP scale factors and the HDOP and VDOP offsets definehow the selected precision 1041 is adjusted according to the prevailingHDOP and VDOP.

FIG. 22 is a flow chart of a method for providing a rover position 1038having a selected precision 1041 to a user. Steps of the method may bein the form of computer-readable instructions stored on or in or carriedby a medium 1200 that may be read by a processor in a particularcomputer or computers for executing the steps. In a step 1202 globalnavigation satellite system (GNSS) observable reference data isdetermined by measurement and computation where the reference dataincludes real time kinematic (RTK) GNSS reference carrier phases. In astep 1204 GNSS observable rover data is determined by measurement andcomputation where the rover data includes real time kinematic (RTK) GNSSrover carrier phases.

The reference and rover data is received at a computer apparatus havingkinematic post processing (KPP) capability in a step 1206. Typically,the computer apparatus is in an office in a different place than theplace where the rover carrier phases were observed and the postprocessing is performed at a later time than the observations of therover carrier phases. In a step 1210 the reference and rover data set ispost processed with KPP to compute a secure position 1010 having anintrinsic precision 1040. The term post process refers to the data setbeing processed at a later time in a different machine than thereference and rover carrier phases were observed. In a step 1220 thesecure position 1010 is dithered with a stream of offset vectors tocompute the user-available position 1038 having the selected precision1041 that is degraded with respect to the intrinsic precision 1040.

FIG. 23 is a flow chart of a method for generating an elongated sequenceof offset vectors for dithering the secure rover position 1010. Steps ofthe method may be in the form of computer-readable instructions storedon or in or carried by a medium 1230 that may be read by a processor ina particular computer or computers for executing the steps. In a step1232 the user-available precision 1041 is selected. In a step 1240 theselected precision 1041 is used to compute a dither level. In a step1242 a sequence seed is generated for a particular data set that is tobe post processed. In a step 1244 a settling time constant is selected.In a step 1246 a settling mean (bias error) is selected for theparticular data set.

A Normal sequence is generated in a step 1248 with the seed. In a step1250 the seeded Normal sequence is elongated with the selected settlingtime constant to generate the elongated sequence of offset vectorshaving the computed dither level as shown in the algorithms 1 or 1b.

FIG. 24 is a flow chart of a method for dithering a secure position 1010to provide a user-available position 1038. Steps of the method may be inthe form of computer-readable instructions stored on or in or carried bya medium 1300 that may be read by a processor in a particular computeror computers for executing the steps. In the step 1210 the secureposition 1010 is computed. In a step 1302 the intrinsic precision 1040of the secure position 1010 is determined from the covariance matrix ofthe position fix or some other way. In an embodiment the intrinsicprecision 1040 has horizontal and vertical components and the horizontalcomponent has east and north components. In steps 1304 and 1306 ahorizontal precision and a vertical precision that are available to theuser are selected.

In a step 1312 a horizontal variance is computed from the selectedhorizontal precision that compensates for the horizontal component ofthe intrinsic precision. Similarly, in a step 1314 a vertical varianceis computed from the selected vertical precision that compensates forthe up component of the intrinsic precision. In a step 1316 thehorizontal variance is scaled according to the east intrinsic precision.Similarly, in a step 1318 the north variance is scaled according to thenorth intrinsic precision.

In steps 1322 and 1324 east and north standard deviations are computedfrom the east and north variances. In a step 1326 an up standarddeviation is computed from the vertical variance. In steps 1332, 1334and 1336 respective sequences of east, north and up offsets are computedhaving the east, north and up standard deviations. In an embodiment therespective Normal east, north and up sequences are generated andelongated with a selected time constant having the above described seedcorresponding to a reference and rover data set. In a further embodimentin steps 1337, 1338 and 1339 the east, north and up sequences,respectively, may be biased to have non-zero average levels. In steps1342, 1344 and 1346 the east, north and up sequences are used to ditherthe east, north and up components of the secure position 1010,respectively, to provide the available rover position 1038 to a user.

FIGS. 25A and 25B are flow charts of a method for selecting theuser-available precision 1041 based on a dilution of precision (DOP) ofthe secure position 1010. Steps of the method may be in the form ofcomputer-readable instructions stored on or in or carried by a medium1360 that may be read by a processor in a particular computer orcomputers for executing the steps. In the steps 1362 and 1364 horizontalDOP (HDOP) and vertical DOP (VDOP) scale factors are selected. In steps1366 and 1368 HDOP and VDOP offsets are selected. In steps 1372 and 1374an HDOP and a VDOP are computed for the constellation of satellites thatis used for computing the secure position 1010.

In steps 1376 and 1378 the HDOP and VDOP of the secure positionsatellites are scaled by the HDOP and VDOP scale factors, respectively.Similarly, in steps 1382 and 1384 the scaled HDOP and VDOP are offset byadding the HDOP and VDOP offsets, respectively.

The media discussed above, 1200, 1230, 1300 and 1360, may have atangible form such as, but not limited to, a compact disk (CD), adigital video disk (DVD), a flash memory, a hard disk, a floppy disk, ora memory chip. The media discussed above may also be in a form of acommunications medium such as, but not limited to, the internet.

Although the present invention has been described in terms of thepresently preferred embodiments, it is to be understood that suchdisclosure is not to be interpreted as limiting. Various alterations andmodifications will no doubt become apparent to those skilled in the artafter having read the above disclosure. Accordingly, it is intended thatthe appended claims be interpreted as covering all alterations andmodifications as fall within the true spirit and scope of the invention.

1. A computer apparatus for post positioning with a selected precision,comprising: a global navigation satellite system (GNSS) post processorto post process reference GNSS carrier phases from a reference systemand rover GNSS carrier phases from a rover receiver to compute a secureposition, said secure position not available to a user, for said roverreceiver; and a vector offset generator to use a selected precision tocompute a dither level for a sequence of offset vectors to degrade anintrinsic precision of said secure position to provide a user-availableposition for said rover receiver at said selected precision; andwherein: the vector offset generator includes an accuracy leveler tocompensate said selected precision for a variation in said intrinsicprecision by computing a smaller said dither level when said intrinsicprecision is less precise.
 2. The apparatus of claim 1, wherein: thepost processor is constructed to perform said post process in adifferent geographical place and at a later time than said rover GNSScarrier phases are observed.
 3. The apparatus of claim 1, wherein: thepost processor includes an intrinsic precision estimator to compute saidintrinsic precision based on covariance matrix components of a positionfix for said secure position.
 4. The apparatus of claim 1, wherein: saidselected precision includes a selected horizontal precision and aselected vertical precision; and said accuracy leveler includes ahorizontal precision compensator to compensate said selected horizontalprecision for a horizontal component of said intrinsic precision toprovide a horizontal component of said dither level, and a verticalprecision compensator to compensate said selected vertical precision fora vertical component of said intrinsic precision to provide a verticalcomponent of said dither level.
 5. The apparatus of claim 4, wherein:said accuracy leveler further includes an east horizontal scaler to usean east part of said horizontal intrinsic precision component to scalesaid horizontal dither level to provide an east dither level; and anorth horizontal scaler to use a north part of said horizontal intrinsicprecision component to scale said horizontal dither level to provide anorth dither level.
 6. The apparatus of claim 1, wherein: said secureposition includes east, north and up components; and further comprising:a random process generator having east, north and up random processorsconstructed to use east, north and vertical components of said ditherlevel to provide east, north and up sequences, respectively, for saidoffset vectors; and a position dither processor to add said east, northand up sequences to said east, north and up components, respectively, ofsaid secure position to provide said user-available position.
 7. Theapparatus of claim 6, wherein: the random process generator includes abias generator to generate east, north and up biases corresponding to aparticular data set of said rover carrier phases to bias mean levels ofsaid east, north and up sequences, respectively.
 8. A computer apparatusfor post positioning with a selected precision, comprising: a globalnavigation satellite system (GNSS) post processor to post processreference GNSS carrier phases from a reference system and rover GNSScarrier phases from a rover receiver to compute a secure position, saidsecure position not available to a user, for said rover receiver; avector offset generator to use a selected precision to compute a ditherlevel for a sequence of offset vectors to degrade an intrinsic precisionof said secure position to provide a user-available position for saidrover receiver at said selected precision; and a DOP scaler to computesaid selected precision by using at least one of a selected DOP scalefactor and a selected DOP offset for processing a dilution of precision(DOP) of a constellation of satellites used for determining said secureposition.
 9. The apparatus of claim 8, wherein: the DOP scaler includesa horizontal precision selector to calculate a horizontal component ofsaid selected precision by multiplying a horizontal component of saidDOP (HDOP) by a selected HDOP scale factor and adding a selected HDOPoffset.
 10. In a computer apparatus a post processing method forproviding a selected precision for a position, comprising: postprocessing reference GNSS carrier phases from a reference system androver GNSS carrier phases from a rover receiver for computing a secureposition, said secure position not available to a user, for said roverreceiver; and computing a dither level for a sequence of offset vectorsfor degrading an intrinsic precision of said secure precision forproviding a user-available position at said selected precision for saidrover receiver; and wherein: computing said dither level includescompensating said selected precision for a variation in said intrinsicprecision by computing a smaller said dither level when said intrinsicprecision is less precise.
 11. The method of claim 10, wherein: postprocessing is performed in a different geographical place and at a latertime than said rover GNSS carrier phases are observed.
 12. The method ofclaim 10, wherein: post processing includes computing said intrinsicprecision based on covariance matrix components of a position fix forsaid secure position.
 13. The method of claim 10, wherein: said selectedprecision includes a selected horizontal precision and a selectedvertical precision; and compensating said selected precision includescompensating said selected horizontal precision for a horizontalcomponent of said intrinsic precision to provide a horizontal componentof said dither level; and compensating said selected vertical precisionfor a vertical component of said intrinsic precision to provide avertical component of said dither level.
 14. The method of claim 13,wherein: computing said dither level further includes using an east partof said horizontal intrinsic precision component for scaling saidhorizontal dither level for providing an east dither level; and using anorth part of said horizontal intrinsic precision component for scalingsaid horizontal dither level for providing a north dither level.
 15. Themethod of claim 10, wherein: said secure position includes east, northand up components; and further comprising steps of: generating east,north and up pseudorandom sequences having east, north and verticalcomponents of said dither level, respectively for said offset vectors;and adding said east, north and up sequences to said east, north and upcomponents of said secure position to provide said user-availableposition.
 16. The method of claim 15, further comprising: generatingeast, north and up biases corresponding to a particular data set of saidrover carrier phases; and biasing mean levels of said east, north and upsequences with said east, north and up biases, respectively.
 17. In acomputer apparatus a post processing method for providing a selectedprecision for a position, comprising: post processing reference GNSScarrier phases from a reference system and rover GNSS carrier phasesfrom a rover receiver for computing a secure position, said secureposition not available to a user, for said rover receiver; computing adither level for a sequence of offset vectors for degrading an intrinsicprecision of said secure precision for providing a user-availableposition at said selected precision for said rover receiver; andcomputing said selected precision by using at least one of a selectedDOP scale factor and a selected DOP offset for processing a dilution ofprecision (DOP) of a constellation of satellites used for determiningsaid secure position.
 18. The method of claim 17, wherein: computingsaid selected precision includes calculating a horizontal component ofsaid selected precision by multiplying a horizontal component of saidDOP (HDOP) by a selected HDOP scale factor and adding a selected HDOPoffset.
 19. A computer-readable non-transitory medium havingcomputer-executable instructions stored or carried thereby that whenexecuted by a processor, perform a method comprising steps of: postprocessing reference GNSS carrier phases from a reference system androver GNSS carrier phases from a rover receiver for computing a secureposition, said secure position not available to a user, for said roverreceiver; and computing a dither level for a sequence of offset vectorsfor degrading an intrinsic precision of said secure precision forproviding a user-available position at said selected precision for saidrover receiver; and wherein: computing said dither level includescompensating said selected precision for a variation in said intrinsicprecision by computing a smaller said dither level when said intrinsicprecision is less precise.
 20. The medium of claim 19, wherein: saidselected precision includes a selected horizontal precision and aselected vertical precision; and compensating said selected precisionincludes compensating said selected horizontal precision for ahorizontal component of said intrinsic precision to provide a horizontalcomponent of said dither level; and compensating said selected verticalprecision for a vertical component of said intrinsic precision toprovide a vertical component of said dither level.
 21. The medium ofclaim 20, wherein: computing said dither level further includes using aneast part of said horizontal intrinsic precision component for scalingsaid horizontal dither level for providing an east dither level; andusing a north part of said horizontal intrinsic precision components forscaling said horizontal dither level for providing a north dither level.22. A computer-readable non-transitory medium having computer-executableinstructions stored or carried thereby that when executed by aprocessor, perform a method comprising steps of: post processingreference GNSS carrier phases from a reference system and rover GNSScarrier phases from a rover receiver for computing a secure position,said secure position not available to a user, for said rover receiver;computing a dither level for a sequence of offset vectors for degradingan intrinsic precision of said secure precision for providing auser-available position at said selected precision for said roverreceiver; and computing said selected precision by using at least one ofa selected DOP scale factor and a selected DOP offset for processing adilution of precision (DOP) of a constellation of satellites used fordetermining said secure position.
 23. The medium of claim 22, wherein:computing said selected precision includes calculating a horizontalcomponent of said selected precision by at least one of multiplying ahorizontal component of said DOP (HDOP) by a selected HDOP scale factorand adding a selected HDOP offset.